Extension of the KLI approximation toward the exact optimized effective potential

Area of Science:

• Quantum Chemistry
• Computational Physics
• Density Functional Theory

Background:

• The optimized effective potential (OEP) is crucial for accurate electronic structure calculations.
• Traditional OEP methods face challenges with Green's functions and numerical stability.
• The Krieger-Li-Iafrate (KLI) approximation offers a practical but not exact solution.

Purpose of the Study:

• To develop a compact and accurate method for solving the OEP integral equation.
• To extend OEP calculations beyond the KLI approximation towards exact solutions.
• To provide a robust framework for calculating spin-unrestricted exchange-correlation potentials.

Main Methods:

• Utilizing a compact form of the OEP integral equation.
• Replacing Green's function integrals with an orbital shift function derived from first-order perturbation theory.
• Employing Dalgarno functions, determined via partial differential equations, to circumvent Green's function numerics.
• Developing a user-friendly method to handle singularities in radial equations for spherically symmetric potentials.

Main Results:

• An accurate OEP solution for the exchange-correlation potential (Vxcσ) is obtained.
• The Dalgarno function is shown to be an explicit integral functional of the exact OEP.
• The OEP equation is reduced to a self-consistent integral equation solvable by iteration.
• First-order iterative corrections beyond the KLI approximation are derived analytically.
• The correction term involves spatially weighted occupied orbital densities and has no adjustable parameters.

Conclusions:

• The Dalgarno function approach provides a significant advancement in solving the OEP equation.
• This method offers a pathway to achieve arbitrarily high accuracy for the optimized effective potential.
• The approach is versatile and applicable to various orbital-dependent exchange-correlation energy functionals.